A general duality theory for uplink and downlink beamforming

Boche, Holger; Schubert, Martin

doi:10.1109/vetecf.2002.1040308

Cited by 151 publications

(134 citation statements)

References 14 publications

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“…where γ k > 0 is the SINR requirement for receiver k. Although problem (P NR ) is nonconvex, it can be transformed to a convex problem and solved globally and efficiently [1][2][3][4]. Because of the finite length of training signal and/or limited feedback bandwidth, perfect CSIT is not available in practice.…”

Section: System Model and Problem Formulationmentioning

confidence: 99%

“…It is well known that if the perfect channel state information is available at the transmitter (CSIT), the optimal transmit beamforming problem can be solved efficiently via convex optimization [1][2][3][4]. However, perfect CSIT is impossible to obtain in practice due to the finite length of training signal and/or limited feedback bandwidth [5,6].…”

Section: Introductionmentioning

confidence: 99%

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Robust SINR-constrained MISO downlink beamforming: when is semidefinite programming relaxation tight?

Song

Shi

Sanjabi

et al. 2012

J Wireless Com Network

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We consider the multiuser beamforming problem for a multi-input single-output downlink channel that takes into account the errors in the channel state information at the transmitter side (CSIT). By modeling the CSIT errors as elliptically bounded uncertainty regions, this problem can be formulated as minimizing the transmission power subject to the worst-case signal-to-interference-plus-noise ratio constraints. Several methods have been proposed to solve this nonconvex optimization problem, but none can guarantee a global optimal solution. In this article, we consider a semidefinite relaxation (SDR) for this multiuser beamforming problem, and prove that the SDR method actually solves the robust beamforming problem to global optimality as long as the channel uncertainty bound is sufficiently small or when the transmitter is equipped with at most two antennas. Numerical examples show that the proposed SDR approach significantly outperforms the existing methods in terms of the average required power consumption at the transmitter.

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Section: System Model and Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust SINR-constrained MISO downlink beamforming: when is semidefinite programming relaxation tight?

Song

Shi

Sanjabi

et al. 2012

J Wireless Com Network

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“…To solve the above problem, we propose an iterative algorithm composed of two steps: First by susing uplink-downlink duality proved in [11][12], we seek proper beamforming matrix and power allocation that make K decentralized receivers achieve individual target SINRs showed in (5) when the total transmission power is max P . Then using beamforming matrix obtained in the first step we minimize the total transmission power based on (4).…”

Section: Downlink Optimazationmentioning

confidence: 99%

“…According paper [11],for given W , the optimal power allocation that minimize the transmission power is characterized by…”

Section: Downlink Optimazationmentioning

confidence: 99%

Downlink physical layer security transmission confronted with synergistic eavesdroping

Zhaoye¹,

Ruimin²

2017

2017 3rd International Conference on Computational Systems and Communications (ICCSC 2017)

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Abstract. The most of existing physical layer security research focus on the situation where decentralized nodes transmit signals to the Base Station(BS). But considering a scenario where nonorthogonal transmission is allowed, when the BS transmits signals to decentralized nodes, the multi-downlinks will interfere each other, decreasing the signal-to-interference-plus-noise ratios (SINRs) at receivers. Focusing on the above problem, this paper optimizes the downlink beamforming and power allocation jointly to meet the SINRs requirement. On this basis, when confronted with synergistic eavesdroping where a malicious jammer helps the eavesdropper to eavesdrop, the BS transmits the artificial noise(AN) to improve the secrecy rate. Then zero-sum game model is proposed to obtain the strategies and corresponding expectation value of the secrecy rate when system reaches the mixed strategy equilibrium. By simulation, this method will obtain a good secrecy rate.

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“…1. Note that this is a special case of the multiple-input multiple-output (MIMO) broadcast channel for which recent progressive developments [7,[16][17][18][19] have led to what is considered as the final solution to the capacity region for the general broadcast channel [20]. In what follows, we use results from [7,20] to obtain and compare the capacity regions of precoding and MUD in the downlink of a CDMA system.…”

Section: Downlink Capacity Regions Of Mud and Precodingmentioning

confidence: 99%

Multiuser TH-precoding for TDD–CDMA over multipath channels

2007

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Nonlinear precoding schemes for downlink time-division duplex -CDMA systems over multipath fading channels, are considered. First, the capacity results of a downlink CDMA system with either multiuser detection or precoding, were obtained and compared. It is seen that the two schemes exhibit similar capacity regions for both sum rate and maximum equal rate, which motivates the development of efficient nonlinear transmitter precoding techniques to reduce the receiver complexity at the mobile units without degrading the system performance. We then develop both bit-wise and chip-wise Tomlinson -Harashima (TH) multiuser precoding methods for downlink CDMA with multipath, to remove multi-user interference, inter-chip interference and inter-symbol interference. Efficient algorithms for multiuser power loading and ordering are also developed. Implementation of the proposed TH-precoding schemes in time-varying channels based on channel prediction is addressed as well. Simulations results are provided to demonstrate the effectiveness of the proposed techniques in suppressing interference in downlink CDMA. IntroductionMultiuser detection (MUD) techniques are considered powerful for interference suppression in CDMA systems, especially in uplinks, where the base-station receiver has the knowledge of all users' spreading sequences and channel states, and can perform sophisticated signal processing [1]. In the downlinks, however, the mobile receiver typically has only the knowledge of its own spreading sequence and channel state. Although adaptive linear MUD (either training-based or blind) can be employed for such scenario, the performance can be limited because of the linear constraint on the detector. Moreover, the power constraint of the mobile calls for simple receiver processing. On the other hand, the precoding schemes for downlink CDMA effiectively transfer the signal processing for interference suppression from the mobile receiver to the base-station transmitter. This approach is feasible if the base-station can estimate the downlink channels of all users [e.g. in systems employing time-division duplexing (TDD) where the uplink and downlink channels are reciprocal]. In [2], a precoding method was proposed which is essentially an implementation of the RAKE receiver at the transmitter. Hence this approach does not attempt to mitigate the multiple-access interference (MAI). Recently, different linear precoding techniques have been proposed to combat MAI and inter-chip interference but without considering inter-symbol interference (ISI) [3,4]. If the ISI is present then the complexity of these techniques becomes prohibitive since the dimension of the matrix filter is proportional to the data frame length multiplied by the number of users (i.e. block processing). More recently, bit-wise linear precoding methods have been proposed to reduce the precoding complexity in the presence ISI [5]. The downlink CDMA is a special case of broadcast channels. There has been significant recent interest in characterising the ca...

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A general duality theory for uplink and downlink beamforming

Cited by 151 publications

References 14 publications

Robust SINR-constrained MISO downlink beamforming: when is semidefinite programming relaxation tight?

Robust SINR-constrained MISO downlink beamforming: when is semidefinite programming relaxation tight?

Downlink physical layer security transmission confronted with synergistic eavesdroping

Multiuser TH-precoding for TDD–CDMA over multipath channels

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